The vEdge solution (described below) is in addition to the Alexa Multi-trigger driver I made available a few days ago, which seems to have proven out the fact that Alexa is having trouble triggering off of switch/contact combo devices.
Connect Amazon Alexa to Samsung SmartThings to control all your SmartThings devices by voice. Step-by-step setup guide with troubleshooting tips.

This article explains what you need to know to get Alexa working with the smart home platform SmartThings, which also runs bulbs, dimmers, and more. You'll need a compatible Amazon device to set this up. Once available on your hub, do an Add device / Scan for nearby devices and a new device called Alexa Multi-Trigger will be created. Open this new device and youll see slots for 19 triggers - each with a name you can edit and a switch. Yes, Alexa works seamlessly with SmartThings! Learn the complete step-by-step setup guide for linking your accounts, discovering devices, and unlocking powerful automation routines.

Furthermore, visual representations like the one above help us fully grasp the concept of Smartthings And Alexa Switching Integration.
Once available on your hub, do an Add device / Scan for nearby devices and a new device called Alexa Multi-Trigger will be created. Open this new device and youll see slots for 19 triggers - each with a name you can edit and a switch.

Furthermore, visual representations like the one above help us fully grasp the concept of Smartthings And Alexa Switching Integration.
Yes, Alexa works seamlessly with SmartThings! Learn the complete step-by-step setup guide for linking your accounts, discovering devices, and unlocking powerful automation routines.
IFTTT quickly automates tasks on SmartThings and Alexa Voice Monkey. Save time, improve productivity, and simplify your workflow. Start for free.Share this using the options below: SmartThings to Alexa Voice Monkey integrations.
Also, in your case its important to understand that your integration will only be one way. You will be able to use smartthings to turn the WiFi switch on and off using this method, but because an Alexa routine cannot be triggered with a switch, you will not be able to use your...